Apple Music files

If you mean DRM protected media from the Apple Music service then this cannot be synced from the library but must instead be added by enabling the Sync Library feature on the phone which works through the cloud. See Use Sync Library with your Apple Music subscription - Apple Support. If on the other hand you want to sync purchased or ripped music from the Apple Music app on your Mac see Sync your iPhone, iPad, or iPod using your computer - Apple Support.

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You can purchase music from the iTunes Store and download it. You can also redownload purchases: Redownload music – Apple Support (AU)